What Is Momentum and How Do You Calculate It?
Momentum is a vector quantity that describes the motion of an object, calculated by multiplying its mass by its velocity. It measures how difficult an object is to stop or redirect, and — unlike kinetic energy — it is always conserved in every collision, whether the objects bounce apart or stick together.
The formula for linear momentum is: p = m × v, where p is momentum in kilogram-meters per second (kg·m/s), m is mass in kilograms, and v is velocity in meters per second. This relationship dates to Isaac Newton's Philosophiæ Naturalis Principia Mathematica (1687), where Newton's second law was originally stated as force equaling the rate of change of momentum, F = Δp/Δt — a more general form of F = ma that still holds even when an object's mass changes, such as a rocket burning fuel.
The SI unit of momentum is the kilogram-meter per second (kg·m/s); unlike force (the newton) or energy (the joule), momentum has no dedicated named unit in the International System of Units. In US customary units, this calculator expresses the same quantity in pound-feet per second (lb·ft/s).
How to Use This Momentum Calculator
Choose Single Object mode to solve the basic p = mv equation for whichever quantity you're missing, or switch to Two-Object Collision mode to see what happens when two moving objects hit each other. Here's what each control does:
- Find Momentum / Mass / Velocity: Pick which quantity to solve for — the calculator rearranges p = mv and asks for the other two values.
- Unit System: Toggle between metric (kg, m/s) and US customary (lb, mph); every result is also shown in the other system.
- Collision Type: Perfectly Inelastic models objects that stick together after impact (like a car crash); Elastic models objects that bounce apart with kinetic energy conserved (like billiard balls).
- Object Velocity: Enter a negative value for an object moving in the opposite direction — momentum is a vector, so direction matters in every collision calculation.
This calculator works in both metric and US customary units. Physics courses worldwide teach momentum in SI units (kg·m/s), while US engineering references sometimes use pound-mass and feet per second (lb·ft/s) — toggle the unit buttons and every field, formula step, and result converts automatically.
Elastic vs. Inelastic Collisions: What's the Difference?
Momentum is conserved in every collision with no external forces acting on the system, but kinetic energy is only conserved in an elastic collision. In a perfectly inelastic collision, the colliding objects stick together and move with one combined velocity, and the kinetic energy "lost" converts into heat, sound, and permanent deformation — it doesn't vanish, it just stops being kinetic energy of the two objects.
| Property | Elastic Collision | Perfectly Inelastic Collision |
|---|---|---|
| Momentum | Conserved | Conserved |
| Kinetic Energy | Conserved | Not conserved — lost to heat, sound, and deformation |
| Objects After Impact | Separate and bounce apart | Stick together, move as one mass |
| Real-World Example | Billiard balls, gas molecules | Car crash, railway cars coupling |
NASA's rocket propulsion equations rely on the same conservation-of-momentum principle: a rocket accelerates forward by expelling propellant mass backward at high velocity, so the momentum the rocket gains exactly equals the momentum the expelled propellant carries away.
Frequently Asked Questions About the Momentum Calculator
What is the formula for momentum?
Momentum (p) equals mass (m) multiplied by velocity (v): p = mv. Momentum is measured in kilogram-meters per second (kg·m/s) in the SI system, or pound-feet per second (lb·ft/s) in US customary units.
What is the difference between momentum and force?
Momentum measures the quantity of motion an object has (mass × velocity), while force measures how quickly that momentum changes over time — Newton's second law states force equals the rate of change of momentum (F = Δp/Δt). A parked truck has zero momentum but can still be acted on by forces such as gravity or friction.
What is the difference between an elastic and an inelastic collision?
In an elastic collision, objects bounce apart and both momentum and kinetic energy are conserved, like billiard balls colliding. In a perfectly inelastic collision, objects stick together and move as one after impact — momentum is still conserved, but kinetic energy is lost to heat, sound, and deformation, as in a car crash.
Is momentum a vector or a scalar quantity?
Momentum is a vector quantity, meaning it has both magnitude and direction — the direction matches the object's velocity. That's why this calculator lets you enter a negative velocity for an object moving in the opposite direction, which is essential for correctly solving collision problems.
How accurate is this momentum calculator?
This calculator uses the exact classical mechanics formulas — p = mv for single-object momentum, and the standard elastic and perfectly inelastic collision equations derived from conservation of momentum and kinetic energy. Results are exact given the inputs; real-world collisions also involve friction, rotation, and material deformation that a simplified model does not capture.